As explained in Applicant's U.S. Pat. No. 5,094,101, a wide variety of methods for weighting and balancing golf clubs are known and have been utilized to some extent in an effort to improve the overall performance, control and handling characteristics of a particular set of golf clubs. Any particular set of clubs includes a plurality of clubs each having a different club head weight, a different shaft length and, consequently, a different overall club weight. The combination of all of these factors requires a golfer to take a different stance and, in effect, a different swing when using each respective golf club. In order to be somewhat proficient at the game of golf, a golfer must therefore practice and attempt to master the various stances and swings associated with using any particular known set of golf clubs. As is well known, all golfers seem to have at least one particular club within any given set which they feel more comfortable with in using and swinging and in which they can more accurately control when hitting any particular golf shot. In total contrast, golfers avoid using other clubs within the same set of golf clubs because they never seem to swing those other clubs properly. Normally, golfers prefer using the shorter irons as proper use and control of these clubs are easier to achieve with some degree of regularity as compared to the longer irons and woods. It is therefore desirable to dynamically balance a particular group or set of clubs based upon the ease and comfortability with respect to swing, performance and control associated with a particular golfer's most preferred club.
Although Applicant's method for dynamically balancing golf clubs using radius of gyration as a controlling parameter as disclosed in U.S. Pat. No. 5,094,101 more accurately describes and simulates the dynamic characteristics associated with swinging a particular golf club and more accurately balances such golf clubs based upon both dynamic as well as static characteristics, such method is somewhat more time consuming and tedious to achieve. Also, golfers have difficulty relating to radius of gyration balancing since such term is somewhat abstract and has no particularly useful physical interpretation or meaning other than being a convenient way of expressing the moment of inertia of the mass of a body in terms of its mass and a length. In an effort to both simplify the overall balancing process and reduce the overall time involved in dynamically balancing golf clubs, Applicant has devised the present compromise method for dynamically balancing golf clubs using equivalent pendulum length instead of radius of gyration as the controlling parameter. The present method still achieves most, if not all, of the benefits and objectives of the dynamic balancing method disclosed in U.S. Pat. No. 5,094,101 including optimizing and improving the overall feel, swing and performance characteristics of a particular set of golf clubs.
Although both Elkins, Jr. U.S. Pat. No. 4,128,242 and Stuff et al U.S. Pat. No. 4,203,598 discuss the period of oscillation of a particular golf club when such club is swung in a pendulum style fashion, and, although Elkins, Jr. U.S. Pat. No. 4,128,242 specifically discloses correlating each club in a particular set such that each club has substantially the same period of oscillation, neither of these two prior art references disclose any method for accomplishing this task other than by empirically measuring or timing the period of oscillation of each respective club. For example, Elkins, Jr. specifically discloses a device in FIG. 5 of U.S. Pat. No. 4,128,242 for swinging two golf clubs together in a pendulum manner in order to compare their respective periods of oscillation. Similarly, the Stuff et al U.S. Pat. No. 4,203,598 likewise discusses suspending a golf club by gimbals at a pivot point approximately 5 inches from the grip end as shown in FIG. 6 of such patent so as to freely swing such golf club in a plane perpendicular to the club face. By so doing, it is possible to empirically determine or measure the period of oscillation of such club by timing each respective swing or oscillation. In fact, in determining the center of percussion using equations 25, 26 and 27 disclosed in the Stuff et al patent, the time constant T is in fact measured empirically by counting the number of complete oscillations n in a given time period t (T=t/n). No other means for computing the period of oscillation is disclosed or even suggested.
Typically, finding the pendulum length of a particular golf club entails swinging the golf club pendulum style as disclosed in both the Elkins, Jr. and Stuff et al references so as to determine the period of oscillation of such club. Once the period of oscillation is empirically determined, one can then use the period of oscillation equation to find the pendulum length of the club, namely, ##EQU2## where T=period of oscillation, or time required for one complete oscillation;
l=the pendulum length; and PA1 g=the gravitational constant (i.e., 32.2 ft/sec.sup.2 or 386.4 in/sec.sup.2). PA1 l=pendulum length measured from the axis of rotation to the center of gravity of the weight of the body; and PA1 g=the gravitational constant (i.e., 32.2 ft/sec.sup.2 or 386.4 in/sec.sup.2). PA1 Q=the shaft or center of percussion length of the club; and PA1 r=the distance between the axis of rotation and the center of gravity of the club. PA1 (1) having a golfer select a reference golf club having all of the optimal parameters and performance characteristics for that particular golfer as set forth and explained in Applicant's U.S. Pat. No. 5,094,101 including ease and comfortability with respect to swing, performance and control of that particular club; PA1 (2) through measuring and balancing, obtaining the shaft or center of percussion length, and the center of gravity location of the reference club as explained in U.S. Pat. No. 5,094,101; PA1 (3) using the equivalent pendulum length equation ##EQU5## where EPL=the equivalent pendulum length of the club, PA1 (4) determining the shaft or center of percussion length of each club to be balanced to the equivalent pendulum length of the reference club; PA1 (5) using the equivalent pendulum length equation, calculate the new center of gravity location for each club to be balanced based upon the selected equivalent pendulum length of the reference club; and PA1 (6) balancing each such golf club to be balanced in a conventional manner at its new center of gravity location based upon the selected pendulum length.
As can be seen from the period of oscillation equation set forth above, the only variable in such equation is the pendulum length. Therefore, once the period of oscillation is determined, one can easily calculate the pendulum length of any particular golf club. As explained below, and based upon the assumption that the swinging motion of a golf club can be simulated by the dynamic equations associated with simple pendulum motion, Applicant has devised a simple mathematical equation to accurately approximate the pendulum length of any particular golf club without first determining the period of oscillation. The use of Applicant's equivalent pendulum length equation avoids the tedious and time consuming method of empirically determining the period of oscillation of any particular golf club by actually timing the same as disclosed in both the Elkins, Jr. and Stuff et al references.